When transferring a goldfish to a new water source, such as a different fish tank, there is an 8% chance that the goldfish will die within the first week.

If we select at random 5 goldfish that have been transferred to a new water source, what is the probability:

(3 marks)

a. that exactly one of them will die within the first week?

(6 marks)

b. that fewer than three of them will die within the first week?

(2 marks)

c. that at least one of them will die within the first week?

(2 marks)

d. Circle True (T) or False (F) for each of the following statements:

T F If we randomly select 6 goldfish that have been transferred instead of 5, the experiment continues to satisfy the conditions for a binomial experiment.

T F John transfers each goldfish to the same bowl. In this case, the chance that a goldfish will die goes up by 1% for each additional goldfish that is selected. This new experiment continues to satisfy the conditions for a binomial experiment.